20. The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows.

Payment ($) Probability Payment ($) Probability 0 .90 2000 .01 400 .04 4000 .01 1000 .03 6000 .01

a. Use the expected collision payment to determine the collision insurance premium that would enable the company to break even.

b. The insurance company charges an annual rate of $260 for the collision coverage. What is the expected value of the collision policy for a policyholder? (Hint: It is the expected payments from the company minus the cost of coverage.) Why does the policyholder purchase a collision policy with this expected value?